Forecasting constraints on the mean free path of ionizing photons at z ≥ 5.4 from the Lyman-α forest flux autocorrelation function

Fluctuations in Lyman-α (Ly α) forest transmission towards high-z quasars are partially sourced from spatial fluctuations in the ultraviolet background, the level of which are set by the mean free path of ionizing photons (λ_mfp). The autocorrelation function of Ly α forest flux characterizes the strength and scale of transmission fluctuations and, as we show, is thus sensitive to λ_mfp. Recent measurements at z ~ 6 suggest a rapid evolution of λ_mfp at z > 5.0 which would leave a signature in the evolution of the autocorrelation function. For this forecast, we model mock Ly α forest data with properties similar to the XQR-30 extended data set at 5.4 ≤ z ≤ 6.0. At each z, we investigate 100 mock data sets and an ideal case where mock data matches model values of the autocorrelation function. For ideal data with λ_mfp = 9.0 cMpc at z = 6.0, we recover $\lambda _{\text{mfp}}=12^{+6}_{-3}$ cMpc. This precision is comparable to direct measurements of λ_mfp from the stacking of quasar spectra beyond the Lyman limit. Hypothetical high-resolution data leads to a $\sim 40~{{\ \rm per\ cent}}$ reduction in the error bars over all z. The distribution of mock values of the autocorrelation function in this work is highly non-Gaussian for high-z, which should caution work with other statistics of the high-z Ly α forest against making this assumption. We use a rigorous statistical method to pass an inference test, however future work on non-Gaussian methods will enable higher precision measurements.